I cannot imagine a genuine astronomer considering these views equivalent to
heliocentrism, at least if we confine our search to anyone born after 1700.
But can one make an ultrasophisticated case for relativity of motion and
claim that the Tychonian system (which is essentially what he promotes) is a
functional equivalent of heliocentrism? I suppose I'd have to say yes, but
then add a couple dozen qualifiers (at least) to indicate in what sense we
might say this: it works just as well if you need to cross the Atlantic in
an open boat without electronic guidance systems. But if you want to land a
probe on the moon, or even orbit one around the earth, you need Newtonian
mechanics, which only made sense historically within a heliocentric theory.
So it really depends a lot on what you want to do with it, bracketing of
course the truth question.